Almost sure H_∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

This paper investigates the almost sure H_∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stability and the H_∞ performance of the system dynamics in the specified sliding surface. A SMC law is designed to guarantee the reachability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme.